Our field in mathematics is the Galois cohomology, a theory by Jean-Pierre Serre and John Tate, which is part of algebra, number theory, algebraic topology and algebraic geometry. The theory has recently known deep expansions with the proof by V. Voevodsky of the Milnor's conjecture (Fiels medal 2002). Our intention is to work one year on this topic with Dr Tamas Szamuely (Renyi Institute, Budapest) by going back to Merkurjev-Suslin's work of the 80's on Galois cohomology, which is the main starting point of Voevodsky's work. Our opinion is that Merkurjev-Sulslin's work has not sufficiently been understood by non-experts, in fact many people are still using it as a "black box". We would like to change the matter by writing a book "Lectures on Merkurjev-Suslin's Theorem" which will include a full proof and presentation of this beautiful result in view of geometrical consequences (cycles in algebraic geometry) and recent work. The book will be based mainly on lectures given by the proposer at Orsay's university and next year in the Renyi institute in Budapest with the collaboration of T.
Szamuely. Such a book does not exist in the present literature and will be clearly useful for people interested in recent progress in Galois cohomology. The proposer and T. Szamuely have some common background, since the scientist in charge received his PHD in Orsy's university. However they have some complementary skills for the project. The proposer is specialist of the topic "Linear Algebraic Group and Galois Cohomology" and T. Szamuely works mainly on the applications of Voevodsky's motivic theories to "Arithmetic Geometry", precisely cycles on algebraic varieties and higher class field theory .Both scientist are confirmed researchers with publications in mathematical journal of high standard, and have a good experience of international collaborations for research and other activities (organisation of workshops, administration of research).
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